, Volume 2, Issue 3, pp 267-277
Date: 04 Feb 2005

How to compute the Wiener index of a graph

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Abstract

The Wiener index of a graphG is equal to the sum of distances between all pairs of vertices ofG. It is known that the Wiener index of a molecular graph correlates with certain physical and chemical properties of a molecule. In the mathematical literature, many good algorithms can be found to compute the distances in a graph, and these can easily be adapted for the calculation of the Wiener index. An algorithm that calculates the Wiener index of a tree in linear time is given. It improves an algorithm of Canfield, Robinson and Rouvray. The question remains: is there an algorithm for general graphs that would calculate the Wiener index without calculating the distance matrix? Another algorithm that calculates this index for an arbitrary graph is given.

Work supported in part by the Research Council of Slovenia, Yugoslavia.
This work was done while both authors were visiting the Simon Fraser University.